3 years ago

Log; (3x+2) = log,(4x-6)

Mathematics

1 answer:

egoroff_w [7]3 years ago

5 0

Answer:

x = 8

Step-by-step explanation:

Using the rule of logarithms

log x = log y ⇔ x = y

Given

log(3x + 2) = log(4x - 6), then

4x - 6 = 3x + 2 ( subtract 3x from both sides )

x - 6 = 2 ( add 6 to both sides )

x = 8

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2 years ago

Ln a+3 + ln a-3 = ln 16

Lilit [14]

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\\\\
and\qquad \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
ln(a+3)+ln(a-3)=ln(16)\implies ln[(a+3)(a-3)]=ln(16)
\\\\\\
ln[a^2-3^2]=ln(16)\impliedby \textit{removing ln() from both sides}
\\\\\\
a^2-9=16\implies a^2=16+9\implies a^2=25
\\\\\\
a=\pm\sqrt{25}\implies a=\pm 5$